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Without solving, match a solution curve of y" + y = f(x) shown in the figure with one of the following functions. ANK Of(x) = 1 O f(x) = e-x O f(x) = ex O f(x) = sin(2x) O f(x) = ex sin(x) O f(x) = sin(x) Briefly discuss your reasoning. We see that the solution is the sum of a sinusoidal term and a term that O is sinusoidal with a different period. O is constant and simply translates the sinusoidal part vertically. goes to coas x→ ∞ and 0 as x→-00. goes to 0 as x→ ∞o and ∞o as x → -0. oscillates with an amplitude that goes to coas x→ ∞o and 0 as x→-00.

Without solving, match a solution curve of y" + y = f(x) shown in the figure with one of the following functions. ANK Of(x) = 1 O f(x) = e-x O f(x) = ex O f(x) = sin(2x) O f(x) = ex sin(x) O f(x) = sin(x) Briefly discuss your reasoning. We see that the solution is the sum of a sinusoidal term and a term that O is sinusoidal with a different period. O is constant and simply translates the sinusoidal part vertically. goes to coas x→ ∞ and 0 as x→-00. goes to 0 as x→ ∞o and ∞o as x → -0. oscillates with an amplitude that goes to coas x→ ∞o and 0 as x→-00.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Without solving, match a solution curve of y" + y = f(x) shown in the figure with one of the following functions. AAMA f(x) = 1 f(x) = ex f(x) = ex O f(x) = sin(2x) f(x) = e* sin(x) O f(x) = sin(x) Briefly discuss your reasoning. We see that the solution is the sum of a sinusoidal term and a term that O is sinusoidal with a different period. O is constant and simply translates the sinusoidal part vertically. goes to co as x → ∞o and 0 as x→-co. goes to 0 as x → ∞o and ∞ as x →→∞0. oscillates with an amplitude that goes to ∞ as x→ ∞ and 0 as x→-00.
Transcribed Image Text:Without solving, match a solution curve of y" + y = f(x) shown in the figure with one of the following functions. AAMA f(x) = 1 f(x) = ex f(x) = ex O f(x) = sin(2x) f(x) = e* sin(x) O f(x) = sin(x) Briefly discuss your reasoning. We see that the solution is the sum of a sinusoidal term and a term that O is sinusoidal with a different period. O is constant and simply translates the sinusoidal part vertically. goes to co as x → ∞o and 0 as x→-co. goes to 0 as x → ∞o and ∞ as x →→∞0. oscillates with an amplitude that goes to ∞ as x→ ∞ and 0 as x→-00.
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